07_(4)_Decimal_Numbers

# 2 add extra zeros if necessary so that each number

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2. Add extra zeros if necessary, so that each number has the same number of decimal places. 3. Add or subtract the digits with the same place value. 4. Insert the decimal point directly below the decimal points of the numbers.

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Decimal Numbers 251
0.325 × + 0_._3_5_ 1625 9_7_5 0.11375 three decimal places two decimal places + five decimal places move each decimal point two places to the right 0.72180.09 72.189 – 728.02 0018 –18 0 So 0.7218 ÷ 0.09 = 8.02. A number is in scientific notation when it is written as x  10 n , where 1 ≤ x < 10 and n is an integer. x 10 n 252 528 000 = 5.28  10 5 75 000 000 = 7.5  10 7 0.000375 = 3.75  10 –4 0.00000091 = 9.1  10 –7 exponent (n Z) decimal part 1  x < 10 exponential part Concepts Examples 7.3 Multiplication and Division of Decimals 7.4Very Large and Very Small Numbers Pre-Algebra 1 To multiply two decimals: 1. Ignore the decimal points and multiply the decimals as whole numbers. 2. Add the number of decimal places in the two dec- imals. The result is the number of decimal places in the product. 3. Insert the decimal point in the product so that it has the correct number of decimal places. To multiply a decimal by a power of 10 such as 10, 100, 1000, etc, count the number of zeros in the power and move the decimal point the same number of places to the right. 0.235 ⋅ 10 = 2.35 3.726 ⋅ 100 = 372.6 32.532 ⋅ 10 3 = 32 532 0.003751 ⋅ 10 5 = 375.1 To divide a decimal by a decimal: 1. Make the divisor into a whole number by moving the decimal point to the right. Count how many places the decimal point moves. 2. Move the decimal point in the dividend the same number of places to the right. Add zeros to the dividend if necessary, before moving the decimal point. 3. Divide using long division. To divide a decimal by a power of 10, count the number of zeros in the power of 10 and move the decimal point the same number of places to the left. 0.65 ÷ 10 = 0.065 121.726 ÷ 10 = 1.21726 0.123 ÷ 10 4 = 0.0000123

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1. 2. 3. Write each decimal in its simplest fraction form. 5. Add the decimals. a . 0.5 b . 0.00 3 c. 1.6 a. 3.4 + 4.7 b. 13.71 + 0.23 d . 3.32 e . 3.00 6 f. 32.624 c. 6.27 + 2.53 d. 4 + 5.3 + 6.03 g . 0.00 025 h . 0.10 001 e. 3.75 + 2.25 + 4.2 W r i te each 1 fraction in decimal form. 3 12 f. 6. Su 0.05 + 0.005 + 0.0001 btract the decimals. 2 d. e 1 0 3 5 c. 100 3 a. c. 5.22 – 4.11 0 b. 9.98 – 8.89 d. 7 – 0.77 100 0 h 1 8 00 00 e. 53.25 – 5.325 f. 0.001 – 0.00001 100000 125 Write each repeating decimal as a fraction. a. 0.2 b. 0.05 c. 0.17 –– –– d. 0.26 e. 1.3 f. 5.016 –– –– –– g. 12.13 –––– –– –––– j. 12.225 Write each fraction as a repeating decimal. 2 7. Find the products. a. 0.5 ⋅ 0.23 c. 0.532 ⋅ 4 e. 0.0175 ⋅ 1000 8. Find the quotients. a. 527.4 ÷ 100 c. 2.43 ÷ 0.27 b. 0.05 ⋅ 0.008 d. 0.0125 ⋅ 8 f. 700.02 ⋅ 0.0003 b. 72.18 ÷ 0.9 d. 0.72 ÷ 0.0006
4. b. c. d. 3 e. 5 3 11 9 17 3 e. 3.06 ÷ 0.03 f. 0.0305 ÷ 0.015 Decimal Numbers 253 9. Write the decimals in descending order. a. 0.5503, 0.5095, 0.5905 b. 0.507, 0.61, 0.595, 0.5079, 0.617 c. 1 , 1 , 1 0.01 0.02 0.04

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