Problem 74 - Prealgebra

Question

Halley's comet was seen from the earth during \(1986 .\) It will be another 76.1 years before it returns. Write 76.1 in words.

Step-by-Step Solution

Answer

Seventy-six and one-tenth.

Step 1: Understand the Problem

The problem asks us to write the number 76.1 in words. This means we need to express both the whole number and the decimal part in a word form.

Step 2: Write the Whole Number in Words

The whole number here is 76. We express 76 in words as 'seventy-six.' This involves breaking down the number into tens and units: 70 as 'seventy' and 6 as 'six.'

Step 3: Write the Decimal Part in Words

The decimal part is .1. When writing this in words, it is expressed as 'one-tenth.' The denominator 'tenth' is used because 1 is in the tenths place.

Step 4: Combine Both Parts in Words

Combine the words for the whole number and the decimal part. Thus, 76.1 is written as 'seventy-six and one-tenth.' The word 'and' is commonly used to link the whole number and the fractional part in words.

Key Concepts

Decimal Numbers

Decimal numbers have two main parts: the whole number part and the decimal fraction. The decimal point acts as a separator between these two parts. Writing decimal numbers in words involves expressing each of these parts clearly.

• Identify the whole number before the decimal point and convert it to words.
• Express the fraction after the decimal point using terms like 'tenths', 'hundredths', etc.

For example, in the number 76.1, the whole number is 76 and the fraction is 0.1, which is one-tenth. The number is written in words as 'seventy-six and one-tenth'.

The decimal point is often followed by the word 'and'. This differentiates the whole number from the fractional part, making it easier to understand each component.

Whole Numbers

Whole numbers are numbers without any fractional or decimal components. They are straightforward to express in written form because they involve simple numerical expressions.

• Read each digit or group of digits according to its place value.
• Use words such as 'thousand', 'hundred', 'ten', 'unit' to denote segments of numbers.

For instance, the number 76 is composed of 70 (seventy) and 6 (six). Thus, we write "seventy-six". When converting whole numbers to words, ensure that the word representation captures all the significant digits of the number ring.

Fractions in Words

Fractions in numbers describe parts of a whole and are expressed using numeric values below or next to each other. Writing fractions in words involves describing both the numerator and the denominator.

• The numerator (the top number) is written with its numerical word form, like one, two, or three.
• The denominator (the bottom number) indicates the division of the whole and uses words like 'third', 'fourth', 'ninth'.

For example, if you have the fraction 1/10, this is read as 'one-tenth'. Learn the terminology for common denominators found in decimal systems, such as 'tenths', 'hundredths', and 'thousandths'.

Combining the whole and fractional components in words allows for clear and comprehensive communication of numerical data, like writing 76.1 as 'seventy-six and one-tenth'.