Bell Ringer 112816

Bell Ringer 112816

Chapter 4 Decimals Review

Writing Decimals Another way to represent part of a whole A number that is written in a system based on multiples of 10. You need to use a decimal point to separate the whole number and the decimal.

Example The decimal three and fifty-two thousandths is shown. 3.052 The decimal three and fifty two thousandths is shown in expanded form: 3 + 5/100 + 2/1000 The same decimal is shown as powers of ten: 3 ones + 0 tenths + 5 hundredths + 2 thousandths

Representing Decimals on a Tenths Grid and a Hundredths Grid Tenths grids and hundredths grids can be used to model decimals and show the connection between fractions and decimals. An entire hundredths grid represents one whole. Each small square represents one- hundredth. An entire tenths grid also represents one whole. Each bar represents one-tenth.

Example

Representing Decimals on a Number Line

Comparing and Ordering Decimals To compare two decimals, compare the digits in each place value from left to right. If the digits in a place value are the same, then move to the right and compare the next place value until you find two different digits to compare. Example The decimals 43.27, 43.532, 43.58, 53.58 are ordered from least to greatest.

Estimating Decimals Using Benchmark Decimals Benchmark decimals, such as 0, 0.5, and 1, are common decimals that can be used to estimate the value of decimals. Example Because the digit in the tenths place is a nine, the decimal 0.9299 is close to 1.

Rounding Decimals To round a decimal to a given place value, look at the digit to the right of the place where you want to round the decimal. If the digit to the right is 4 or less, round down. If the digit to the right is 5 or greater, round up. Example To round 68.2468 to the nearest hundredth, look at the digit in the thousandths place. The digit in the thousandths place is 6. Because 6 is greater than 5, round up. So, 68.2468 rounded to the nearest hundredth is 68.25.

Writing Fractions as Decimals

Estimating Sums and Differences of Decimals To estimate the sum or difference of decimals, first round each decimal to the nearest whole number. Then, add or subtract. Example Estimate 45.42 + 124.924 - 99.02. 45.42 + 124.924 - 99.02 5= 45 + 125 – 99 = 71

Adding and Subtracting Decimals When adding or subtracting decimals, be sure to line up the decimal points. Doing so helps to ensure that the digits in the same place value are being added or subtracted correctly. a. 8.964 + 12.05 b. 125.03 - 6.1032 8.964 125.0300 12.050 6.1032 21.014 118.9268

Multiplying Decimals When multiplying decimals, the number of decimal places in the product is equal to the sum of the decimal places in the factors. Estimating the product helps to check if a product is reasonable. Example The estimate of the product for the expression 6.13 × 9.87 to the nearest whole number is shown. Then, the product of the multiplication expression is shown. Estimate: 6.13 X 9.87 ≈ 6 x 10 = 60

Actual product: 6.13 X 9.87 4291 4904 5517 60.5031 6.13 x 9.87 = 60.5031 Estimating first made it easier to determine where to place the decimal point in the product.

Dividing Whole Numbers

First estimate how many eights are in 41,816. Think: 5000 x 8 = 40,000 First estimate how many eights are in 41,816. Think: 5000 x 8 = 40,000. Therefore, take the difference of 41,816 and 40,000. The difference is 1816. Next, estimate how many eights are in 1816. Think: 200 x 8 = 1600. Therefore, take the difference of 1816 and 1600. The difference is 216. Then, estimate how many eights are in 216. Think: 20 x 8 = 160. 30 x 8 =5 240 — that’s too much! Therefore, take the difference of 216 and 160. The difference is 56. You know that 8 x 7 = 56. Finally, add the factors to find the quotient. The quotient is 5227.

Dividing Whole Numbers with Quotients that Have Remainders Not all numbers divide evenly into other numbers. When a divisor does not evenly divide into the dividend, the quotient contains a remainder. Remainders can be written as fractions, decimals, or as a whole number. Depending on the situation, the remainder can be ignored because all that needs to be calculated are whole numbers.

Dividing Decimals When dividing decimals, first multiply the dividend and the divisor by the power of ten that makes the divisor a whole number. Then divide. Be sure to line up the decimal point in the quotient with the decimal point in the dividend. Estimating the quotient helps to check if the quotient is reasonable. Example The estimate of the division expression 15.19 ÷ 4.9 to the nearest whole number is shown. Then, the quotient of the division expression is shown. Estimate: 15.19 ÷ 4.9 ≈ 15 ÷ 5 = 3

Actual quotient: