Problem 27 - Prealgebra

Question

Multiply. Round to nearest hundredth if necessary. $$0.07(2,000)$$

Step-by-Step Solution

Answer

The product is 140.

Step 1: Understand the Problem

We need to multiply 0.07 by 2,000 and then round the result to the nearest hundredth if required. This involves a simple multiplication and a rounding operation.

Step 2: Perform the Multiplication

Calculate the product of 0.07 and 2,000 by directly multiplying them. \[ 0.07 imes 2000 = 140 \]

Step 3: Check for Rounding

Since the result of the multiplication is 140, which is an integer, we do not need to round to the nearest hundredth, as there are no decimal places present. The number 140.00 is already at the nearest hundredth.

Key Concepts

Rounding

Rounding is a technique used to simplify numbers, making them easier to work with while maintaining their approximate values. In the context of decimals, rounding often involves adjusting the number to a specific decimal place, such as the nearest tenth, hundredth, or thousandth.
When rounding to the nearest hundredth:

• Look at the third decimal place (thousandths place).
• If the digit in this place is 5 or greater, increase the second decimal place (hundredths place) by 1.
• If the digit is less than 5, leave the second decimal place unchanged.

For example, if you have the number 140.567 and you want to round it to the nearest hundredth, you would look at the 7 in the thousandths place. Since it is more than 5, you round up the 6 in the hundredths place to 7, resulting in 140.57. However, if the original result is a whole number, like 140, there’s no need for further rounding.

Decimals

Decimals are a way to represent numbers that are not whole, using a point (decimal point) to separate the whole part from the fractional part. Decimals can express values between integers and are quite common in measurements, currency, and scientific data.
Understand decimals with these basics:

• The number on the left of the decimal point is the integer part, representing whole units.
• The number on the right after the decimal point signifies parts of a whole.

Decimal places are counted from the decimal point. The first position is tenths, the second is hundredths, and so on. This means that, in the number 0.07, the 0 is in the tenths place, and the 7 is in the hundredths place. In multiplication, decimals work by directly multiplying the numbers while accounting for the placement of the decimal point.
For instance, multiplying 0.07 by 2,000 involves treating 0.07 as its exact decimal value, where the position of the decimal point will influence the final product.

Basic Arithmetic Operations

Basic arithmetic operations include addition, subtraction, multiplication, and division. These are the fundamental techniques in mathematics used to handle numbers.

• Addition involves combining numbers to get a sum. For example, 3 + 4 equals 7.
• Subtraction is taking one number away from another. For instance, 5 - 2 equals 3.
• Multiplication is repeated addition. To multiply 0.07 by 2,000 means you add 0.07 a total of 2000 times, resulting in 140 after simplification.
• Division involves distributing one number into equal parts. For example, 10 divided by 2 equals 5.

Each operation has its own set of rules that must be followed to arrive at the correct result. Multiplication, like in the exercise 0.07 times 2000, requires focusing on both the numbers and any decimal points involved, ensuring the values are correctly calculated and represented.