Problem 30 - Prealgebra

Question

Multiply. Round to nearest hundredth if necessary. $$900(0.06)\left(\frac{1}{4}\right)$$

Step-by-Step Solution

Answer

The result is 13.5, no rounding necessary.

Step 1: Multiply the First Two Numbers

Start by multiplying the first two numbers: \(900\) and \(0.06\). \[900 \times 0.06 = 54\]

Step 2: Multiply the Result by the Third Number

Now, take the result from Step 1 and multiply it by \(\frac{1}{4}\). \[54 \times \frac{1}{4} = 54 \div 4 = 13.5\]

Step 3: Round the Final Result

Round the result from Step 2 to the nearest hundredth if necessary. However, \(13.5\) is already rounded to the nearest hundredth, so no further rounding is needed.

Key Concepts

Multiplication

Multiplication is one of the basic arithmetic operations that involves calculating the total of one number being added a certain number of times. For example, multiplying two numbers such as 900 and 0.06 means you are calculating what 0.06 of 900 is.
Let's break down the multiplication process using our specific example of 900 and 0.06:

• Multiplying by a decimal means finding a part of the whole, so here, you find 6% of 900.
• To do this, simply multiply as if you're dealing with regular integers: 900 multiplied by 6 gives 5400.
• Since we're working with a decimal (0.06), shift the decimal point two places to the left, resulting in 54.

Understanding this step is essential because it sets a foundation for handling more complex arithmetic with decimals and fractions.

Fractions

Fractions represent a part of a whole and are expressed as one integer over another, like \( \frac{1}{4} \). They are fundamental in different operations, including multiplication. When you multiply by a fraction, you can think of it as "taking a fraction of something." In our exercise:

• We multiply 54 by the fraction \( \frac{1}{4} \). Think of 54 as the "whole" that we are taking a quarter of.
• This is equivalent to dividing 54 by 4, because \( \frac{1}{4} \) means "one part out of four equal parts."
• Hence, multiplying by \( \frac{1}{4} \) efficiently discovers that quarter value of 54, resulting in 13.5.

Fractions help with the division of wholes into smaller parts, showcasing a key aspect of real-world applications where things are split into portions and segments.

Decimal Rounding

Decimal rounding involves adjusting a decimal number to make it simpler or to conform to a standard level of precision. This is especially crucial in financial calculations and science. When rounding to the nearest hundredth, you look two decimal places to the right. Here's a simple guide:

• If the digit in the hundredth place is followed by 5 or more, round up.
• If it's followed by 4 or less, keep it unchanged.

In our case, 13.5 doesn't require further rounding as there's only one digit after the decimal. It's already at the precision needed. Understanding this step ensures clarity and precision, which is important in correctly representing figures in various contexts.