Problem 90 - Prealgebra

Question

Determine which of the two given statements is true. 0.000681 < 0.00043174 or 0.000681 > 0.00043174

Step-by-Step Solution

Answer

0.000681 > 0.00043174 is true.

Step 1: Compare Decimal Places

First, align the two decimal numbers vertically and compare them place by place. Start from the leftmost digit (excluding the leading zeros).

Step 2: Compare Leading Digits

Compare the first non-zero digit of both numbers. For 0.000681, it is 6, and for 0.00043174, it is 4. Since 6 is greater than 4, the number 0.000681 is greater than 0.00043174.

Step 3: Confirm the Comparison

Since 6 is the comparison digit and it's greater than 4, the statement 0.000681 > 0.00043174 is true. Thus, the first statement 0.000681 < 0.00043174 is false.

Key Concepts

Understanding Decimal Places

Decimals are used to express numbers that fall between integers, and a "decimal place" refers to the position of a number after the decimal point. For instance, in the number 0.000681, the digit 6 is in the sixth decimal place. Each digit in a decimal stands for a power of ten, so it's important to pay attention to where each digit falls.
Decimal places provide precision. For example, a measurement of 0.123 is less precise than 0.123456. The more decimal places a number has, the more accurate it can be. When comparing decimal numbers like 0.000681 and 0.00043174, it is crucial to align the numbers correctly by their decimal points and compare place by place.

• Align numbers by their decimal points.
• Compare digits starting from the leftmost non-zero digit.

This method ensures that you assess each digit correctly by its weight, or its power of ten.

Grasping Inequality in Decimals

Inequality simply means the relationship between numbers where they are not equal. In mathematics, inequality symbols such as "<" and ">" are used to compare two numbers or expressions.
When you're dealing with decimal numbers, understanding inequality is important as it helps you establish which number is larger or smaller. For the given exercise, comparing 0.000681 and 0.00043174, the '>' symbol tells us that 0.000681 is larger than 0.00043174.

• "<" means less than.
" means greater than.

Understanding these symbols helps to make sense of and solve numerical comparison problems.

Effective Number Comparison

Number comparison is a basic yet essential math skill that allows you to determine the relative size of numbers. When comparing numbers, especially decimals, aligning the numbers properly and examining each digit is key.
In cases like our exercise with the numbers 0.000681 and 0.00043174, after aligning the decimal points, compare digit by digit. The first digit that's not the same gives you the essential information you need. Since 6 is greater than 4, we can conclude that 0.000681 is larger.

• Align decimal numbers by their points.
  
• Start comparing from the leftmost non-zero digit.
  
• The first differing digit indicates which number is greater or lesser.
  

This helps in drawing accurate conclusions about the size of two numbers, ensuring you understand their value relative to one another.