Question

Determine the number of decimal places in each approximate number. $$5.882$$

Short answer

The number 5.882 has 3 decimal places.

Step-by-step solution

Identify Decimal Places

To determine the number of decimal places in an approximate number, count the digits appearing after the decimal point. In the given number 5.882, the digits after the decimal point are 882.

Count Decimal Places

Count each digit after the decimal point individually. There are three digits after the decimal point, which means there are three decimal places.

Key concepts

Approximate Numbers

Numbers that are not exact but are close to the actual value are known as approximate numbers. In real-world scenarios, we often use these numbers when an exact value is either unavailable or unnecessary. For instance, when you measure the length of a table with a ruler, your measurement might be 120.5 centimeters. That decimal, .5, signifies that your measurement isn't perfectly exact—it's approximate.

To express precision, or sometimes the lack of it, approximate numbers often contain decimal places. Consider your smartphone's battery life at any given moment; the display might show 76.4% battery remaining. That .4 is an approximate representation suggesting that the battery life is not exactly 76%, but it's around that figure. Approximate numbers, therefore, help us navigate daily life with figures that are practical and easily communicable instead of overly precise and unwieldy.

Identifying Decimal Places

Understanding how to identify decimal places is fundamental in math and everyday calculations. When you see a number with a decimal point, the position of each digit to the right of that point represents a specific decimal place. The first digit after the decimal represents the tenths place, the second represents the hundredths place, and so forth.

Let's take the price of gas for example. A price displayed as \(3.459 per gallon indicates that the price is not simply \)3 per gallon, but three dollars and just under 46 cents - with the 9 representing the thousandths place, which might seem insignificant but is crucial for accurate billing. As you practice, the longer the string of numbers after the decimal, the more places you have to identify, keeping in mind each position has a unique place value.

Counting Decimal Places

Counting decimal places is a straightforward process once you've identified them. After noting the decimal point, you simply count each digit that follows it. This count is necessary for many mathematical tasks, such as rounding numbers to a specific place value or performing operations with significant figures. It can also be important when dealing with money, measurements, and statistics where precision to a certain degree is required.

For example, when cooking and a recipe calls for 1.375 liters of water, you're dealing with three decimal places. It's indicating the quantity needed is more precise than if it was written as 1.3 liters. Each decimal place is representative of a fractional part of a whole, and thus when you count them, you acknowledge the level of precision implicated in the number.