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Chapter 2: Problem 73

Round the number to the given place value. \(6.061745 ;\) thousandths

Short Answer

Expert verified
The number \(6.061745\) rounded to the thousandths place is \(6.062\).

Step by step solution

01

Identify the Digit at the Given Place Value

Look at the digit in the thousandths place. Here, \(6.061745\) has '1' in its thousandths place.
02

Look at the Digit Next to the Identified Digit

The next digit to '1' (in the ten-thousandths place) is '7'.
03

Decide to Round Up or Stay the Same

Since '7' is greater than or equal to 5, round it up. So, '1' becomes '2'.
04

Truncate the Number

Now truncate the number after the thousandths place, we get the rounded number \(6.062\).

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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 a decimal is crucial for rounding. In the number given, which is 6.061745, each digit to the right of the decimal represents a fraction of ten. The layout of decimal places typically looks like this:
  • Tenths place: first digit to the right of the decimal, representing parts of ten
  • Hundredths place: second digit, representing parts of a hundred
  • Thousandths place: third digit, representing parts of a thousand
For the number 6.061745, the third digit after the decimal point is '1', which is in the thousandths place. This means it represents 1/1000 or 0.001. This position helps us understand not only the size of the decimal fraction but also its significance in rounding up or down.
Place Value
Place value is the fundamental concept of understanding the position of a digit in a number, which gives it value. For decimal numbers, every place to the right of the decimal point also has a unique place value. Starting from the rightmost side of the decimal
  • The tenths place, containing 6 in our number 6.061745, holds a value of 0.6.
  • The hundredths place has 0, representing 0.00.
  • The thousandths place contains 1, which we've identified as 0.001 in value.
This concept is essential not only for basic arithmetic but also for tasks like rounding numbers effectively. By knowing each position's place value, you can accurately assess the weight or significance it contributes to the entire number. Calculations involving decimals require careful understanding of how each digit contributes to the total value of the number.
Rounding Rules
Rounding decimals involves specific rules that help determine how we adjust numbers to a desired level of precision. The main goal is to simplify numbers without significantly altering their value. Here's how we apply these rules:
  • Identify the digit at the place value you're rounding to. In this example, the thousandths place.
  • Look at the digit immediately to the right of that place. This digit informs whether the number rounds up or remains unchanged.
  • Apply the rounding rule: If the digit is 5 or higher, round the digit in the selected place value up by one. If it's 4 or less, leave the digit as it is.
For instance, in the number 6.061745, looking to the ten-thousandths place, the digit 7 suggests we round the thousandths digit 1 up to 2. The outcome of rounding helps in making decisions easier by working with simpler numbers, especially useful in daily life tasks or data interpretation.

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Most popular questions from this chapter

Convert the fraction to a decimal. Place a bar over repeating digits of a repeating decimal. $$6 \frac{3}{5}$$

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