Review of Place Values in Decimal Numbers A decimal number includes a decimal point and digit(s) to the right of the decimal point. Saying a decimal number aloud is very similar to saying a whole number aloud. How would you say the number 1375.2316 aloud? Once again, you need to know the place values of the digits. The place values of decimal numbers are related to the place values of whole numbers. The whole number part (the part to the left of the decimal point) has the same place values as before. What we re interested in now are the place values of the decimal part. 1 3 7 5. 2 3 1 6 no th side th side Note how the place value names start from the decimal point. Going to the left is ones, tens, hundreds, thousands, etc. as before. Going to the right is tenths, hundredths, thousandths, ten-thousandths, etc. The pattern going to the right or the left from the decimal point is the same but there are two big differences: The place values to the right of the decimal point all end in th. There is no such thing as oneths.
To say the number 1375.2316, say the whole number part, the word and, (representing the decimal point), and the number to the right of the decimal point, followed by the name of the place value of the last digit: One thousand three hundred seventy-five and two thousand sixteen ten-thousandths 1375. 2016 name of place value of the 6 -------------------------------------------------------------------------------------------- PRACTICE: 1) Name the digit in the following 2) Write the following numbers places in the number 10,234.56789 in words. a) tens a) 241.3 b) tenths b) 27.008 c) ten-thousands c) 500.06 d) thousandths d) 3.07021 e) ones f) hundredths 3) Write the following numbers with digits: a) six and nine tenths b) one hundred two and three hundredths c) twelve and three thousand two hundred forty-eight ten-thousandths d) seven hundred six thousandths --------------------------------------------------------------------------------------------------------------------------------- 2
Rounding Decimal Numbers Rounding with decimals is very similar to rounding with whole numbers. As with whole numbers, you are asked to round a number to a given place value. Everything to the right of the given place value becomes a zero, and the digit in the given place value either stays the same or goes up one. There is one big difference between rounding with decimals and rounding with whole numbers. Zeroes at the end of a decimal number are dropped, while zeroes at the end of a whole number must remain. 3600 36 100,000 1 Dropping zeroes at the end of a whole number changes the number. 36.00 = 36 1.00000 = 1 Dropping zeroes at the end of a decimal does not change the meaning. One way to think of it is to consider the number thirty-six dollars. It can be written equally well one of two ways: $36 = $36.00 Any zero at the very end of a decimal number can be dropped: 18.25000 = 18.2500 = 18.250 = 18.25 Ex. 1. A sprinter ran a race in 7.354 seconds. How long did the sprinter take, rounded to the nearest tenth of a second? given place value Go to the given place value and 7.354 look at the first digit to its right. look here 3
If it s greater than or equal to 5, 7.354 round up (increase the digit in the 5 = 5, so increase the 3 to a 4. given place value by 1). If it s less than 5, leave the digit in the given place value alone. Change all digits to right of the given 7.400 place value into zeroes. THIS IS AN INTERMEDIATE STEP WHICH YOU DON T ACTUALLY WRITE DOWN. Drop all zeroes at the end of the 7.4 decimal part. Final answer. Ex. 2. Round 7.354 to the nearest hundredth. given place value Go to the given place value and 7.354 look at the first digit to its right look here If it s less than 5, leave the digit 7.354 in the given place value alone. 4 is less than 5, so leave 5 as is Drop all zeroes to the right of the 7.35 given place value. Sometimes you re asked to round a decimal number to a place value which is not in the decimal part. Ex. 3. Round 1,294.6374 to the nearest hundred. given place value Go to the given place value and 1,294.6374 look at the first digit to its right look here 9 is greater than or equal to 5, 1,3. _ so increase the 2 to a 3. 4
Zeroes to the left of the decimal must be included. 1,300. _ Zeroes to the right of the decimal 1,300 are dropped. -------------------------------------------------------------------------------------------- PRACTICE: 1) Round 62.15723 to the nearest 2) Round 1.608541 to the nearest a) tenth a) hundred-thousandth b) ten-thousandth b) thousandth c) hundredth c) tenth d) thousandth d) hundredth 3) Round 17,289.3615 to the nearest 4) Round 841.9508 to the nearest a) ten a) hundredth b) hundredth b) one c) thousand c) tenth d) one d) ten e) tenth e) thousandth f) thousandth f) hundred -------------------------------------------------------------------------------------------- 5
ANSWERS TO PRACTICE PROBLEMS Page 2 1. a. 3 b. 5 c. 1 d. 7 e. 4 f. 6 2. a. two hundred forty-one and three tenths b. twenty-seven and eight thousandths c. five hundred and six hundredths d. three and seven thousand twenty-one hundred-thousandths 3. a. 6.9 b. 102.03 c. 12.3248 d..706 Page 3 1. a. 62.2 b. 62.1572 c. 62.16 d. 62.157 2. a. 1.60854 b. 1.609 c. 1.6 d. 1.61 3. a. 17,290 b. 17,289.36 c. 17,000 d. 17,289 e. 17,289.4 f. 17,289.362 4. a. 841.95 b. 842 c. 842.0 d. 840 e. 841.951 f. 800 6
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