Question

q3_unit 3_lesson 15/16/17 multiply and divide decimals elena multiplies 0.06 × 0.5 on a calculator. the calculator shows a product of 0.03. elena says the calculate must be broken because multiplying tenths by hundredths always gives a product in thousandths. is elena’s calculator broken? type your answer to explain your thinking.

Explanation:

Step1: Analyze the decimals' place values

0.06 is 6 hundredths (since \(0.06=\frac{6}{100}\)) and 0.5 is 5 tenths (since \(0.5 = \frac{5}{10}\)).

Step2: Multiply the fractions

Multiply the two fractions: \(\frac{6}{100}\times\frac{5}{10}=\frac{6\times5}{100\times10}=\frac{30}{1000}\).

Step3: Simplify the fraction

Simplify \(\frac{30}{1000}\) to decimal form. \(\frac{30}{1000}=0.03\) (because dividing 30 by 1000 moves the decimal point three places to the left, but 30 has two digits, so we get 0.03). Also, note that when multiplying decimals, the number of decimal places in the product is the sum of the decimal places in the factors. 0.06 has 2 decimal places, 0.5 has 1 decimal place, so the product should have \(2 + 1=3\) decimal places. But \(0.03\) can be written as \(0.030\) which has three decimal places (the trailing zero after the 3 is a placeholder for the thousandths place). So the calculator's result of 0.03 is correct because 0.03 is equivalent to 0.030 (in thousandths place value when considering the correct number of decimal places for the product).

Answer:

Elena's calculator is not broken. When multiplying \(0.06\) (6 hundredths) and \(0.5\) (5 tenths), we calculate \(\frac{6}{100}\times\frac{5}{10}=\frac{30}{1000} = 0.03\) (or \(0.030\) when showing the thousandths place). The product \(0.03\) is equivalent to \(0.030\) (with three decimal places, matching the sum of the decimal places in the factors: \(2 + 1=3\)). So the calculator's result is correct.