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Chapter 4: Problem 71

Round to the nearest thousandth. $$ 17.0014 $$

Short Answer

Expert verified
17.001

Step by step solution

01

Identify the Thousandth Place

Locate the thousandth place in the number. The thousandth place is the third digit to the right of the decimal point. In the number 17.0014, the digit at the thousandth place is 1.
02

Look at the Digit to the Right

Check the digit to the immediate right of the thousandth place to decide if you need to round up or keep it the same. For 17.0014, the digit to the right of the thousandth place is 4.
03

Apply the Rounding Rule

If the digit to the right of the thousandth place is 5 or more, increase the thousandth place by 1. If it is less than 5, keep the thousandth place the same. Since 4 is less than 5, the thousandth place remains unchanged.
04

Write the Rounded Number

Write the new number including only up to the thousandth place. Therefore, 17.0014 rounded to the nearest thousandth is 17.001.

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Key Concepts

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

thousandth place
In decimal notation, the thousandth place is an important aspect when rounding numbers. It is the third digit to the right of the decimal point. Understanding its position aids in precise rounding. For instance, in the number 17.0014, the digit at the thousandth place is 1.
rounding rules
Rounding rules are simple but crucial for accurate calculations. These rules determine whether to round a number up or keep it the same. Here's a quick guide when rounding decimals:
  • If the digit to the right of your rounding place is less than 5, you round down, keeping the digit the same.
  • If the digit is 5 or more, you round up, increasing the digit by one.
For example, in 17.0014, the digit to the right of the thousandth place is 4 (which is less than 5). Hence, the thousandth place remains 1.
decimal places
Decimal places help in representing numbers more precisely. They are the digits to the right of the decimal point. Each place is worth ten times less than the place to its left. Knowing this, the positions are:
  • The first place is the tenths.
  • The second place is the hundredths.
  • The third place is the thousandths.
For a number like 17.0014, it extends up to four decimal places.
mathematics rounding
Mathematics rounding is an essential skill. By following specific rounding rules, you ensure your results are both simplified and accurate. For instance, 17.0014, when rounded to the nearest thousandth, simplifies to 17.001. Always identify the place you are rounding to and follow the rounding rules and you'll get consistent results. This practice is key in many mathematical applications.

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Most popular questions from this chapter

Add. $$ \begin{array}{r} 13.72 \\ 9.112 \\ 6542.7908 \\ +\quad 23.901 \\ \hline \end{array} $$

The average American eats \(688.6 \mathrm{lb}\) of fruits and vegetables in a year. What is the average consumption in one day? (Use 1 year \(=365\) days.) Round to the nearest tenth of a pound.

The five largest oneday point gains in the Dow Jones Industrial Average are listed in the table below. Find the average of the five greatest point gains; round the answer to the nearest hundredth of a point. $$ \begin{array}{|c|c|} \hline \text { DATE } & \begin{array}{c} \text { DJIA HIGHEST } \\ \text { POINT GAINS } \end{array} \\ \hline 10 / 13 / 2008 & 936.42 \\ 10 / 28 / 2017 & 889.35 \\ 8 / 26 / 2017 & 619.07 \\ 11 / 13 / 2008 & 552.60 \\ 3 / 16 / 2000 & 499.19 \\ \hline \end{array} $$

Estimate by rounding as directed. $$ \begin{aligned} &2.678-0.445\\\ &\text { nearest tenth } \end{aligned} $$

Estimate. Indicate which of the choices is an appropriate estimate. \(7.4 \times 8.9\) a) 95 b) 63 c) 124 d) 6
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