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Chapter 5: Problem 68

Divide. Round the answer to the indicated place value. Use the rounded quotient to check. $$-54.9 \div 3.7 \text { tenths }$$

Short Answer

Expert verified
-14.8

Step by step solution

01

- Divide the numbers

First, perform the division \( -54.9 \div 3.7 \) to find the quotient. \[ -54.9 \div 3.7 = -14.83783783783784 \]
02

- Round to tenths place

Look at the quotient found in step 1: -14.83783783783784. The tenths place is the first digit after the decimal point. Round the quotient to the nearest tenths place.\[ -14.83783783783784 \approx -14.8 \]
03

- Verify the rounded quotient

Multiply the rounded quotient (-14.8) by the divisor (3.7) to check the accuracy. \[ -14.8 \times 3.7 = -54.76 \] When rounded to the same precision as the original number (-54.9), the result (-54.76) is reasonably close to -54.9, confirming our rounding was accurate.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

division process
In prealgebra, understanding the division process is essential. Division is the process of splitting a number into equal parts. In this exercise, we need to divide -54.9 by 3.7. First, identify which number is the dividend (the number being divided) and which is the divisor (the number you are dividing by). In our case:
  • Dividend: -54.9
  • Divisor: 3.7
Perform the division: \[ -54.9 \div 3.7 = -14.83783783783784 \]It's often helpful to use a calculator for such calculations to ensure precision. Yet, always double-check your work. Next, let鈥檚 move on to rounding the result.
rounding numbers
Rounding numbers makes them simpler by retaining only the most significant digits. This helps in approximate calculations and easier comprehension. For rounding to the tenths place, observe the first digit after the decimal point:
  • The quotient from the previous step was -14.83783783783784.
  • The tenths digit is the first digit after the decimal: 8 in -14.83783783783784.
To round correctly:1. Look at the digit immediately to the right of the tenths place.
2. If that digit is 5 or greater, round the tenths place up by one. Otherwise, keep it the same.
Here, the next digit is 3, less than 5. Therefore, we round down:\[ -14.83783783783784 \approx -14.8 \]
verification of results
Verification is a critical step to ensure the accuracy of our rounding. It involves reversing the operation to check if we are close to the original value. For our exercise, multiply the rounded quotient by the divisor:\[ -14.8 \times 3.7 = -54.76 \]Compare this product with the original dividend -54.9. Given the slight discrepancy is acceptable within the context of rounding errors. Thus:
  • The original value: -54.9
  • The product after verification: -54.76
These values are close enough, confirming our division and rounding processes were correct. Remember, small differences are expected and considered normal in approximate calculations.

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