Problem 88 - Prealgebra

Question

Determine which of the two given statements is true. 514.873553 < 514.86374 or 514.873553 > 514.86374

Step-by-Step Solution

Answer

514.873553 > 514.86374 is true.

Step 1: Compare Whole Numbers

Start by examining the whole numbers of both decimal values. Both numbers have the same whole number part of 514.

Step 2: Compare Tenths Place

Check the tenths place of each number. Both numbers have 8 in the tenths place, so they are equal up to tenths.

Step 3: Compare Hundredths Place

Examine the hundredths place. The first number has 7, while the second number has 6. Since 7 is greater than 6, 514.873553 is greater than 514.86374.

Key Concepts

Whole Numbers

When comparing decimal numbers, the first step is always to look at the whole numbers. The whole number is the part of the number that is in front of the decimal point.
Think of whole numbers as the backbone of the decimal number. In both 514.873553 and 514.86374, the whole number is 514.
Since both numbers have the same whole number, they are equal at this stage. Remember, if the whole numbers were different, the number with the larger whole number would be greater, regardless of the digits after the decimal point.
This is why whole numbers are the primary basis for comparison.

Tenths Place

Once the whole numbers are checked and found the same, move to the tenths place. The tenths place is the first digit immediately after the decimal point. It represents how many tenths are in the number.
In this example, both numbers have an 8 in the tenths place.
This indicates that up to the tenths place, both numbers are equal.
The tenths place is crucial because it can often be enough to decide which number is greater. If one number had a larger digit in the tenths place, it would be the larger number.

Hundredths Place

If needed, after the tenths place, we check the hundredths place for further comparison. The hundredths place is the second digit after the decimal point. It shows how many parts out of a hundred are in the number.
Here, 514.873553 has a 7 in the hundredths place, while 514.86374 has a 6.
This shows that 514.873553 is larger because 7 (hundredths) is greater than 6.
The hundredths place becomes important when tenths are identical, offering a more detailed level to measure the exactness of decimals. Always remember, each place after the decimal has value, reflecting more precision in comparisons.