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Chapter 1: Problem 18

Round the given number to the specified decimal place 0.077777 to the thousandths place

Short Answer

Expert verified
0.078

Step by step solution

01

Identify the Thousandths Place

The thousandths place is the third digit to the right of the decimal point. In the number 0.077777, the digit in the thousandths place is 7 (the third 7 in 077777).
02

Determine If Rounding Is Necessary

Look at the digit immediately to the right of the thousandths place to see if rounding is needed. This digit is the fourth 7 in 077777. Since it is 5 or greater, we need to round up.
03

Perform the Rounding

To round 0.077777 to the thousandths place, increase the digit in the thousandths place by 1. Therefore, the third 7 becomes 8, making the number 0.078.

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Key Concepts

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

Decimal Places
When dealing with decimal numbers, the digits to the right of the decimal point represent decimal places. These are crucial in determining the precision of a number. Each position signifies a fraction of powers of ten. For example,:
  • The first position right after the decimal point is the tenths place (1/10).
  • The second position is the hundredths place (1/100).
  • The third position is the thousandths place (1/1000).
Understanding these places helps when you need to round numbers accurately. It determines how precise your number representation is.
Imagine a number like 0.345. Here, 3 is in the tenths place, 4 is in the hundredths place, and 5 is in the thousandths place. Therefore, decimal places are instrumental in pinpointing the level of detail you preserve in mathematical calculations.
Thousandths Place
The thousandths place is an essential concept for rounding and accuracy. It is the third digit to the right of the decimal point. Number 0.077777 serves as an example. Here, the first 0 is in the tenths place, the subsequent 7s fill the hundredths and thousandths places respectively; thus, the third 7 is in the thousandths place.
Understanding which digit occupies the thousandths place can impact both precision and the value of calculations. If rounding is required to this specific position, you focus on the digits to its right to decide whether it should remain the same or change.
Rounding Rules
Rounding is a valuable tool in mathematics, simplifying numbers while retaining their significant essence. For rounding, existing rules guide whether to round up or down. Here's a concise breakdown of these rules:

  • Identify the target digit to round. For 0.077777, the aim is to the thousandths place..
  • Look at the digit immediately to the right of this target. If it is 5 or greater, round up by adding one to the target digit.
  • If it is less than 5, maintain the target digit as it is.
Applying these rules correctly changes 0.077777 to 0.078. This ensures that the rounded number is as close as possible to the original, while fulfilling precision requirements.

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