Problem 87 - Algebra 1: Concepts and Skills

Question

Write the fraction as a decimal rounded to the nearest thousandth. $$ -\frac{18}{35} $$

Step-by-Step Solution

Answer

The decimal equivalent of the fraction -18/35 rounded to the nearest thousandth is -0.514

Step 1: Divide Numerator by Denominator

Divide the numerator by the denominator. In this case, divide -18 (the numerator) by 35 (the denominator). The division operation will not hold sign so, -18 / 35 = -0.514285714.

Step 2: Round off to the Nearest Thousandth

Here, the value is raised to the nearest thousandth. The third, fourth, and fifth places after the decimal are 14 and 2 respectively, so the digit in the fourth place (1) does not change as the digit in the fifth place (2) is less than 5. Therefore, the rounded off value becomes -0.514.

Key Concepts

Rounding Decimals

Rounding decimals is a method used to simplify a number while maintaining its value close to the original. It's particularly handy when you need to reduce a number to fit a certain precision. In the context of the solution provided, we discussed rounding a decimal to the nearest thousandth. Think of each place after the decimal point as a ranking for how precise you are.

The nearest thousandth is the third digit to the right of the decimal. Here's a simplified approach:

• Identify the digit in the thousandths place.
• Check the digit immediately to the right (ten-thousandths place).
• If this digit is 5 or greater, increase the thousandths place digit by one.
• If it's less than 5, keep the thousandths place digit as it is.

In our exercise, the digit in the thousandths place was 4, and the next digit was 2, which is less than 5. Therefore, the number remained "-0.514" after rounding.

Numerator and Denominator

Fractions are a way to represent parts of a whole. Fractions consist of two main parts: the numerator and the denominator. Understanding these components is crucial in fraction to decimal conversion.

• The **numerator** is the top part of the fraction. It represents how many parts we have.
• The **denominator** is the bottom part. It indicates how many parts make up a whole.

For example, in the fraction \(-\frac{18}{35}\), 18 is the numerator, and 35 is the denominator. The numerator -18 tells us we have 18 parts, and the denominator 35 indicates that 35 such parts constitute a whole. For converting fractions to decimals, remember that the numerator is the number you're dividing, and the denominator is the number you're dividing by.

Division in Mathematics

Division is a core mathematical operation used to distribute a number into equal parts. It's heavily involved in converting fractions to decimal form. Essentially, you're determining how many times the denominator fits into the numerator.

• Division helps break down a fraction to a simpler form, like a decimal.
• With fractions like \(-\frac{18}{35}\), it means dividing -18 by 35.
• The resulting decimal portrays the quotient, or the result of the division, rounding it if needed.

In our specific example, performing the division of -18 by 35 yielded approximately \(-0.514285714\). Through rounding, this becomes \(-0.514\). This decimal represents the portion of the whole that -18 is in relation to 35.