Question

Explain how to estimate the product of two decimals. Give an example with two decimals estimated and correct actual answers.

Answer 1

To estimate the product of two decimals like 2.48 and 6.3, you can round them to 2.5 and 6, respectively, and multiply to get an estimate of 15. The actual product, 15.687, should be rounded to match the least number of significant figures, resulting in 16.

Step-by-step explanation:

To estimate the product of two decimals, you can round each decimal to a specific place value that's easier to work with and then multiply the rounded numbers. For multiplication and division, the rule is to limit the significant figures in the answer to the same number as the measurement with the least number of significant figures.

Example:

If you want to estimate the product of 2.48 and 6.3, you might round 2.48 to 2.5 and 6.3 to 6. When multiplied together, 2.5 times 6 equals 15. The actual product of 2.48 times 6.3 is 15.687, which would be rounded to 16 to reflect two significant figures, as the number 6.3 has two significant figures.

When following this method:

• Estimate 2.48 to 2.5 (rounding to the nearest tenth).
• Estimate 6.3 to 6 (rounding to the nearest whole number).
• Multiply the estimated values: 2.5 x 6 = 15.
• The actual answer is 15.687, round to 16 to match the least number of significant figures.

Significant Figures

Always remember to round your final answer to the same number of significant figures as the measurement with the least number of significant figures involved in the multiplication or division.

Answer 2

Our main goal is to estimate the product of two decimals. The key idea behind it is to approximate each number to a reasonable number that is easier to calculate. Take for example the product of 15.5 and 6.5. We could approximate each number to the closes integer (16 and 7). So we can multiply 16 times 7 to get an estimate (112).

However, 15.5 is between 10 and 20 which is are numbers that are easy to multiply by while calculating. So you can aproximate 15.5 to 20. Also, we can aproximate 6.5 to 5, so another estimate of this product is 20 times 5, which is 100.

In this case, 15.5 times 6.5 is 100.75, so we can see that the estimates are relatively close to the real value