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Chapter 3: Problem 17

Round each number to the indicated place value. $$ 0.7049 \text { (thousandths) } $$

Short Answer

Expert verified
0.7049 rounded to the thousandths place is 0.705.

Step by step solution

01

Identify the Place Value to Round To

Look at the fourth digit after the decimal point since the thousandths place is the fourth position after the decimal point. For the number 0.7049, the fourth digit is a 9, which is in the thousandths place.
02

Determine the Rounding Digit

Identify the digit to the right of the thousandths place to determine if the thousandths digit will round up or stay the same. In 0.7049, the digit to the right of the thousandths place is 9.
03

Apply Rounding Rules

Since the digit to the right of the thousandths place (9) is 5 or higher, round the thousandths digit up. Increase the thousandths digit (4) by 1 to get 5, which gives us 0.705. If the digit were less than 5, we would keep the thousandths digit the same.

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Key Concepts

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

Thousandths Place
Understanding the 'thousandths place' in decimals is critical for students when learning about place value and rounding. In a decimal number, the thousandths place refers to the third position to the right of the decimal point. For instance, in the number 0.7049, the digit 4 is in the thousandths place. To give you a clearer picture, the place value chart for this number is as follows:
  • Tenths: 0
  • Hundredths: 7
  • Thousandths: 4

Grasping this concept is essential as it is the cornerstone for performing more advanced operations with decimals, specifically when rounding them to a specified precision.
Place Value
Place value is a fundamental concept in mathematics that defines the value of a digit based on its position within a number. Each position in a number has a specific value such as ones, tens, hundreds for whole numbers, and tenths, hundredths, thousandths for decimals. To conceptualize this, consider the following example: the number 0.7049 can be broken down into
  • 0 units (ones)
  • 7 tenths
  • 0 hundredths
  • 4 thousandths
  • 9 ten-thousandths

Together, each digit contributes its place value to the number's total value. Comprehending place value is vital for students as it underlies all arithmetic operations and provides a firm foundation for understanding the decimal system.
Rounding Rules
Rounding decimals involves applying specific rules to approximate a number to a certain level of precision. The process starts by identifying the place to which you want to round. Once that's done, the following guidelines are used:
  • If the digit in the next place to the right is less than 5, the digit in the place you are rounding to stays the same.
  • If the digit in the next place to the right is 5 or more, you increase the digit in the place you are rounding to by one.

For example, to round 0.7049 to the thousandths place, you'll look at the digit beyond the thousandths (in this case, the 9 in the ten-thousandths place) and decide to round up the number in the thousandths place from 4 to 5 due to the rule just mentioned, resulting in the rounded number 0.705.

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Most popular questions from this chapter

Round each number to the indicated place value. $$ 6,473 \text { (hundreds) } $$

Multiply each pair of numbers. \(13.5 \cdot 2.9\)

Round each number to the indicated place value. $$ 0.7049 \text { (hundredths) } $$

Subtract each pair of numbers. $$ 82.78-67.024 $$

Write each number. seven and fifty-six thousandths
See all solutions

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