Problem 91 - Prealgebra

Question

Determine which of the two given statements is true. ?15.188392 < ?15.187157 or ?15.188392 > ?15.187157

Step-by-Step Solution

Answer

?15.188392 > ?15.187157 is true.

Step 1: Compare the Whole Numbers

First, observe the whole number parts of both numbers. In this case, both numbers have the same whole number part, which is 15.

Step 2: Compare the Decimal Parts

Next, focus on comparing the decimal parts since the whole numbers are identical. The decimals are 0.188392 and 0.187157.

Step 3: Compare from the First Decimal Place

Start by comparing from the first decimal place after the dot. The first decimal digit for both numbers is 1. Since they are equal, we move to the next decimal digit.

Step 4: Compare the Second Decimal Place

Examine the second digit after the decimal. For both numbers, the second digit is 8. Since these are also equal, proceed to the next digit.

Step 5: Compare the Third Decimal Place

Look at the third digit after the decimal point. For both numbers, it is 8 again. Thus, we need to check the next decimal digits.

Step 6: Compare the Fourth Decimal Place

Compare the fourth digits. 3 for the first number and 7 for the second number. Since 3 is less than 7, ?15.188392 is less than ?15.187157.

Key Concepts

Decimal Place Value

Understanding decimal place value is crucial when dealing with numbers having fractional parts. This system helps us identify the value of each digit in a decimal number. Let's break it down:

• The first digit after the decimal point is the tenths place.
• The second digit is the hundredths place.
• The third digit is the thousandths place, and so on.

For example, in the number 15.188392, the digit '1' is in the tenths place, '8' in the hundredths place, and '8' in the thousandths place. Each digit has a value based on its position relative to the decimal point.

By understanding decimal place value, you can easily compare digits at the same place value to determine which of two decimal numbers is larger or smaller. This concept is essential in various mathematics problems.

Number Comparison

Comparing numbers, especially decimals, involves looking at each digit systematically from left to right. Here's how you can compare decimal numbers effectively:

Start by examining the integer part of each number. If these are equal, which is the case for 15.188392 and 15.187157, proceed to compare the digits one by one, starting from the tenths place.

• If the digits are the same, move to the next digit and continue the comparison.
• The first time you find different digits, the decimal with the larger digit is the greater number.

For the example 15.188392 and 15.187157, both have the same first three decimal digits (1, 8, and 8). However, at the fourth place, '3' is less than '7', indicating that 15.188392 is smaller than 15.187157.

This method ensures accuracy when determining the relative size of decimal numbers.

Mathematics Problem Solving

In mathematics, problem solving often involves a methodical approach to tackle challenges. When presented with a problem, it's critical to follow a structured strategy:

• Identify what is being asked. In this case, we need to determine which of two decimal numbers is greater.
• Use place value to inform your comparison, as decimal digits directly influence the numbers' values.
• Check each digit systematically, as explained in previous sections.

This systematic approach, demonstrated through comparing 15.188392 and 15.187157, not only helps solve specific arithmetic problems like these but also builds a foundation for tackling more complex mathematical challenges.

Practicing these steps enhances logical reasoning and numerical fluency, critical skills in math and beyond.