What is the place value of the 7 in 324.2671? A) thousands B) thousandths C) hundreds D) hundredths
A) thousands Incorrect. The digit 7 is to the best of the decimal point, which method that the is less than one and on the th side. The exactly answer is thousandths. B) thousandths Correct. The digit 7 is three decimal locations to the best of the decimal point, which way that the is in the thousandths place. C) hundreds Incorrect. The number 7 is 3 decimal areas to the appropriate of the decimal point, which means that it is in the thousandths place. D) hundredths Incorrect. The digit 7 is three decimal locations to the ideal of the decimal point, which way that the is in the thousandths place. Reading Decimals The easiest method to review a decimal number is to read the decimal fraction part as a fraction. (Don’t leveling the fraction though.) expect you have actually 0.4 grams of yogurt in a cup. You would certainly say, “4 one per 10 of a gram of yogurt,” as the 4 is in the one per 10 place. Note that the denominator of the fraction written in fraction kind is always a power of ten, and the number of zeros in the denominator is the very same as the number of decimal locations to the best of the decimal point. Check out the instances in the table below for more guidance. Decimal Notation | Fraction Notation | Word Form | 0.5 | | five tenths | 0.34 | | thirty-four hundredths | 0.896 | | eight hundred ninety-six thousandths | Notice that 0.5 has actually one decimal place. Its identical fraction, , has a denominator the 10—which is 1 complied with by one zero. In general, once you are converting decimals to fractions, the denominator is always 1, followed by the variety of zeros that correspond to the variety of decimal areas in the initial number. Another means to identify which number to location in the denominator is to use the place value that the critical digit there is no the “ths” part. Because that example, if the number is 1.458, the 8 is in the thousandths place. Take away the “ths” and also you have a thousand, so the number is composed as . Example | Problem | Write 0.68 in word form. | 0.68 = = sixty-eight hundredths | Note that the number is review as a fraction. Also keep in mind that the denominator has actually 2 zeros, the very same as the number of decimal places in the original number. | Answer The number 0.68 in word form is sixty-eight hundredths. | | | | Recall that a An expression in which a totality number is merged with a suitable fraction. For example 5 is a mixed number. ")">mixed number is a combination of a entirety number and also a fraction. In the situation of a decimal, a mixed number is additionally a mix of a entirety number and also a fraction, wherein the portion is composed as a decimal fraction. To read mixed numbers, to speak the entirety number part, the word “and” (representing the decimal point), and the number to the ideal of the decimal point, followed by the name and the location value of the last digit. You deserve to see this prove in the chart below, in i beg your pardon the critical digit is in the ten thousandths place. Another way to think around this is with money. Expect you salary $15,264.25 because that a car. Girlfriend would read this together fifteen thousand, two hundred sixty-four dollars and also twenty-five cents. In this case, the “cents” method “hundredths that a dollar,” therefore this is the exact same as speak fifteen thousand, 2 hundred sixty-four and twenty-five hundredths. A couple of more examples are displayed in the table below. Decimal Notation | Fraction Notation | Word Form | 9.4 | | Nine and four tenths | 87.49 | | Eighty-seven and forty-nine hundredths | 594.236 | | Five hundreds ninety-four and also two hundreds thirty-six thousandths | Example | Problem | Write 4.379 in native form. | 4.379 = = four and also three hundreds seventy-nine thousandths | The decimal portion is check out as a fraction. Note that the denominator has actually 3 zeros, the very same as the variety of decimal locations in the original number. | Answer The number 4.379 in word type is four and three hundred seventy-nine thousandths. | | | | Write 2.364 in word form. A) two and also three hundreds sixty-four hundredths B) two and also three hundred sixty-four thousandths C) two thousand 3 hundred sixty-four D) 3 hundred sixty-four tenths and two Show/Hide Answer
A) two and also three hundreds sixty-four hundredths Incorrect. You suggested the dorn decimal place in your answer. The exactly answer is two and also three hundreds sixty-four thousandths. B) two and three hundreds sixty-four thousandths Correct. 2.364 is the same as , for this reason in addition to the totality number 2, you have actually three hundred sixty-four thousandths. C) 2 thousand 3 hundred sixty-four Incorrect. Friend ignored the decimal point. The correct answer is a decimal; in this case, two and also three hundred sixty-four thousandths. D) 3 hundred sixty-four tenths and two Incorrect. You suggested the not correct decimal ar in her answer, and the whole number part should it is in mentioned prior to the decimal part. The correct answer is two and three hundreds sixty-four thousandths. Writing decimal as streamlined Fractions As you have seen above, every decimal can be composed as a fraction. To convert a decimal come a fraction, ar the number after the decimal allude in the numerator of the fraction and place the number 10, 100, or 1,000, or another power that 10 in the denominator. Because that example, 0.5 would be written as . You’ll notice that this portion can be more simplified, as reduces come , i m sorry is the final answer. Let’s get an ext familiar with this relationship between decimal places and zeros in the denominator by feather at several examples. Notification that in every example, the variety of decimal places is different. Example | Problem | Write 0.6 as a simplified fraction. | 0.6 = | The critical decimal location is tenths, so usage 10 for your denominator. The number of zeros in the denominator is constantly the very same as the variety of decimal places in the initial decimal. Simplify the fraction. | Answer 0.6 = | | | | Let’s look at at an example in which a number with two decimal areas is composed as a fraction. Example | Problem | Write 0.64 as a streamlined fraction. | 0.64 = | The last decimal place is hundredths, so usage 100 for her denominator. The number of zeros in the denominator is constantly the very same as the number of decimal places in the original decimal. Simplify the fraction. | Answer 0.64 = | | | | Now, examine just how this is done in the example listed below using a decimal with digits in 3 decimal places. Example | Problem | Write 0.645 together a simplified fraction. | 0.645 = | Note the there space 3 zeros in the denominator, i m sorry is the same as the variety of decimal locations in the original decimal. Simplify the fraction. | Answer 0.645 = | | | | You can write a portion as a decimal also when there space zeros come the appropriate of the decimal point. Right here is an example in which the just digit greater than zero is in the thousandths place. Example | Problem | Write 0.007 together a simplified fraction. | 0.007 = | Note that 7 is in the thousandths place, for this reason you create 1,000 in the denominator. The number of zeros in the denominator is constantly the very same as the number of decimal areas in the initial decimal. The fraction cannot be simplified further. | Answer 0.007 = | | | | When composing decimals higher than 1, girlfriend only require to adjust the decimal component to a portion and store the entirety number part. Because that example, 6.35 have the right to be written as 6 . Example | Problem | Write 8.65 as a simplified blended fraction. | 8.65 = 8 = 8 | Rewrite 0.65 together Note that the variety of zeros in the denominator is two, i beg your pardon is the very same as the number of decimal areas in the original decimal. Then simplify by dividing numerator and denominator by 5. | Answer 8.65 = | | | | Write 0.25 as a fraction. A) B) C) D) Show/Hide Answer
A) Incorrect. Girlfriend may have put the number from the tenths location in the numerator, and the number from the hundredths place in the denominator. The exactly answer is . B) Correct. The number 0.25 can be written as , i m sorry reduces to . C) Incorrect. Friend probably confused the numerator and also the denominator. The correct answer is . D) Incorrect. Girlfriend may have actually put the number from the tenths ar in the denominator, and also the digit from the hundredths place in the numerator. The correct answer is . Writing Fractions together Decimals Just as you can write a decimal together a fraction, every portion can be composed as a decimal. To write a portion as a decimal, division the molecule (top) of the fraction by the denominator (bottom) that the fraction. Use long division, if necessary, and note whereby to location the decimal suggest in her answer. Because that example, to compose as a decimal, divide 3 by 5, i beg your pardon will an outcome in 0.6. Example | Problem | Write as a decimal. | −1 0 0 | Using lengthy division, you deserve to see that separating 1 by 2 outcomes in 0.5. | Answer = 0.5 | | | | Note the you could also have thought about the trouble like this: , and also then solved for ?. One method to think about this difficulty is the 10 is five times greater than 2, for this reason ? will have to be 5 times greater than 1. What number is five times greater than 1? 5 is, so the systems is . Now look at a more facility example, where the final digit the the prize is in the thousandths place. Example | Problem | Write as a decimal. | −2 4 60 − 56 40 − 40 0 | Using long division, you can see that dividing 3 through 8 results in 0.375. | Answer = 0.375 | | | | Converting from fountain to decimals sometimes results in answers with decimal number that start to repeat. For example, converts come 0.666, a repeating decimal, in i beg your pardon the 6 repeats infinitely. You would write this as , through a bar end the an initial decimal number to show that the 6 repeats. Look in ~ this example of a trouble in which 2 consecutive number in the price repeat. Example | Problem | Convert to a decimal. | − 3 3 70 − 66 40 − 33 70 − 66 4 0. | Using lengthy division, you can see that separating 4 by 11 results in 0.36 repeating. Together a result, this is written with a line end it together . | Answer = | | | | With numbers greater than 1, keep the whole number part of the blended number together the entirety number in the decimal. Then usage long division to transform the fraction part come a decimal. For example, can be created as 2.15. Example | Problem | Convert to a decimal. | − 8 20 − 20 0 2 + 0.25 = 2.25 | Knowing that the entirety number 2 will stay the same during the conversion, emphasis only ~ above the decimal part. Using lengthy division, you have the right to see that splitting 1 through 4 outcomes in 0.25. Now bring ago the whole number 2, and also the resulting portion is 2.25. | Answer = 2.25 | Tips top top Converting fractions to Decimals To compose a portion as a decimal, divide the molecule (top) of the portion by the denominator (bottom) the the fraction. In the situation of repeating decimals, compose the repeating digit or digits with a line end it. For example, 0.333 repeating would be written as .
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| Summary Decimal notation is another method to write numbers the are less than 1 or that combine whole numbers v decimal fractions, sometimes called mixed numbers. When you compose numbers in decimal notation, you deserve to use prolonged place-value chart that contains positions because that numbers much less than one. You can write numbers composed in portion notation (fractions) in decimal notation (decimals), and also you deserve to write decimals together fractions. You can always convert in between fractional notation and decimal notation.
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