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Chapter 4: Problem 74

Round to the nearest thousandth. $$ 0.1161 $$

Short Answer

Expert verified
0.116

Step by step solution

01

Identify the Thousandth Place

Locate the thousandth place in the number 0.1161. The thousandth place is the third digit to the right of the decimal point, which is the number 6 in this case.
02

Identify the Next Digit

Look at the digit to the right of the thousandth place to decide whether to round up or keep the same. The digit in the fourth place to the right of the decimal is 1.
03

Apply Rounding Rules

If the digit in the place immediately following the thousandth place (here, 1) is 5 or greater, round up the digit in the thousandth place. Otherwise, keep the same digit. Since 1 is less than 5, do not change the digit in the thousandth place.
04

Write the Rounded Number

After applying the rounding rules, write the number. The thousandth digit 6 remains the same. Therefore, 0.1161 rounded to the nearest thousandth is 0.116.

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Key Concepts

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

thousandth place
Rounding numbers requires understanding different decimal places. The thousandth place is one of these key positions. Starting from the decimal point, the sequence of decimal places is: tenths, hundredths, and then thousandths. The thousandth place is the third digit to the right of the decimal point. For example, in the number 0.1161, the thousandth place is occupied by the digit 6.
rounding rules
Rounding numbers helps to simplify them while keeping their value close to the original number. Specific rules guide this process. When rounding to the nearest thousandth, you look at the digit immediately to the right of the thousandth place. This helps determine whether to round the thousandth place digit up or keep it the same.
If the digit next to the rounding place is 5 or greater, you round up the digit in the thousandth place. For digits less than 5, you keep the digit unchanged. For example, in 0.1161, the digit in the thousandth place is 6, and the next digit is 1. Since 1 is less than 5, the digit 6 in the thousandth place stays the same, resulting in 0.116.
decimal places
Understanding decimal places is fundamental in grasping the rounding concept. A decimal number consists of a whole number part and a fractional part, separated by a decimal point. Decimal places refer to the positions of digits to the right of the decimal point.

These places follow a specific order: tenths, hundredths, thousandths, and so on. Each place value is ten times smaller than the previous one. For instance, in the number 0.1161:
  • '1' is in the tenths place,
  • '1' is in the hundredths place,
  • '6' is in the thousandths place, and
  • '1' is in the ten-thousandths place.
Proper recognition of these places helps students accurately apply rounding rules and achieve the correct simplified number.

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Most popular questions from this chapter

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