Problem 713 Order each pair of numbers, usin... [FREE SOLUTION]

Chapter 1: Problem 713

Order each pair of numbers, using < or >. \(0.91___0.901\)

Short Answer

Expert verified

0.91 > 0.901

Step by step solution

- Compare the Whole Number Parts

Examine the digits to the left of the decimal point in each number. Both numbers, 0.91 and 0.901, have a whole number part of 0.

- Compare the Digits after the Decimal

Look at the digits immediately after the decimal point. The first digit after the decimal in both numbers is 9.

- Compare the Tenths Place

Since the first digits after the decimal (tenths place) are the same, proceed to the next digit. The second digit in 0.91 is 1, whereas in 0.901 it is 0.

- Determine the Order

Since 1 (in the hundredths place of 0.91) is greater than 0 (in the hundredths place of 0.901), we have 0.91 > 0.901.

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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 accurately comparing and ordering numbers. Decimals are numbers with a dot, or decimal point, separating the whole number part from the fractional part. Each digit to the right of the decimal point represents a different place value:

The first digit is the tenths place
The second is the hundredths place
The third is the thousandths place

In the problem, we compared 0.91 and 0.901. Both numbers have the same whole number part (0). When we look at the tenths place, they both have a 9. However, moving to the hundredths place, 0.91 has a 1 while 0.901 has a 0. This means that 0.91 has a higher hundredths place value, making it larger.

inequality symbols

Inequality symbols help us show the relationship between two numbers. The two primary symbols used are:

'<' means 'less than'
'>' means 'greater than'

For example, when comparing 0.91 and 0.901, we determined that 0.91 is greater. We use the '>' symbol to properly write the relationship: 0.91 > 0.901. Conversely, we would use '<' if 0.91 were smaller. Understanding these symbols is key to correctly expressing how one number relates to another.

ordering numbers

Ordering numbers involves arranging them from smallest to largest or vice versa. To successfully do this with decimals, follow these steps:

Compare the whole number parts
If these are equal, compare the tenths place
If the tenths are also equal, move to the hundredths place, and so on

In our example, 0.91 and 0.901 have the same whole number (0) and tenths place (9). The difference is in the hundredths place, where 0.91 has a 1 and 0.901 has a 0. This tells us that 0.91 is greater than 0.901. By following these steps, you can accurately order any set of decimals.

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91影视

Order each pair of numbers, using < or >. \(0.91___0.901\)

Short Answer

Step by step solution

- Compare the Whole Number Parts

- Compare the Digits after the Decimal

- Compare the Tenths Place

- Determine the Order

Key Concepts

decimal place value

inequality symbols

ordering numbers

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