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Chapter 1: Problem 712

Order each pair of numbers, using < or >. \(0.86___0.69\)

Short Answer

Expert verified
0.86 > 0.69

Step by step solution

01

Compare the Whole Numbers

Begin by looking at the whole numbers to the left of the decimal point. Both numbers have 0 as the whole number component, so they are equal in this respect.
02

Compare the Tenths Place

Next, compare the digits in the tenths place (the first digit to the right of the decimal point). In 0.86, the digit is 8, and in 0.69, the digit is 6. Since 8 is greater than 6, we can already determine the relationship between the two numbers.
03

Conclusion

Since 8 in 0.86 is greater than 6 in 0.69, we can conclude that 0.86 > 0.69.

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Key Concepts

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

Decimal Place Value
Understanding decimal place value is crucial for comparing and ordering decimals. A decimal number consists of a whole number part and a fractional part, separated by a decimal point.
Each place position after the decimal point represents a power of ten, getting smaller as you move to the right.
For instance, in the number 0.86:
  • The digit 8 is in the tenths place, meaning 8/10 or 0.8.
  • The digit 6 is in the hundredths place, meaning 6/100 or 0.06.
As such, understanding the place value helps us compare decimals efficiently.
When comparing decimals, we start from the left and move right, comparing place values one at a time until we find which number is greater or lesser.
Ordering Numbers
Ordering numbers involves arranging them from smallest to largest or vice versa. To order decimals:
1. **Compare Whole Numbers**: Start by comparing the digits to the left of the decimal point. If they are the same, move to the next step.
2. **Compare Decimal Places**: Compare the digits in the tenths place first.
  • In 0.86 vs. 0.69, both numbers have the whole number 0.
  • Next, look at the tenths place: the digit 8 in 0.86 and 6 in 0.69. Since 8 is greater than 6, 0.86 is greater than 0.69.
3. **Continue as Needed**: If the digits in the tenths place are the same, move to the hundredths place, and so on.
This method ensures that you compare each decimal accurately and order the numbers correctly.
Greater Than and Less Than Symbols
The symbols > and < are used to compare two values.
  • **Greater Than (>):** The symbol > means that the number on the left is larger than the number on the right.
  • **Less Than (<):** The symbol < means that the number on the left is smaller than the number on the right.
For example:
In the comparison 0.86 > 0.69, we see that 0.86 has a larger value than 0.69 when looking at the tenths place, so we use the > symbol.
Learning to properly use and understand these symbols is essential for accurately comparing and ordering numbers.
Practice by comparing different pairs of numbers, and verify your understanding by explaining the reasoning behind each comparison step.

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