Video: Finding a Decimal between Two Given Decimals and Converting It to a Fraction and a Percentage

Which of the following expresses a decimal between 0.35 and 0.95, its fraction in simplest form, and its percentage form? [A] 0.4, 2/5, 40%. [B] 0.4, 40/100, 40%. [C] 0.4, 2/5, 35%. [D] 0.45, 40/100, 35%. [E] 0.45, 2/5, 4%.

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Video Transcript

Which of the following expresses a decimal between 0.35 and 0.95, its fraction in simplest form, and its percentage form?

Let’s firstly consider the two different decimals that we have, 0.4 and 0.45. Both of these do indeed lie between 0.35 and 0.95. In order to convert a decimal into a percentage, we multiply by 100. 0.4 multiplied by 100 is equal to 40, and 0.45 multiplied by 100 is equal to 45. Our digits moved two places to the left. This means that we can immediately rule out options (C), (D), and (E), as their decimals and percentages do not match.

Both option (A) and option (B) have the decimal 0.4 and the percentage 40 percent. This means that we have an equivalent percentage form. Our next step is to work out which of the fractions is written in simplest form. The word “percent” means out of 100. So 40 percent can be written as 40 out of or over 100. This suggests that option (B) might be the correct answer.

However, 40 over 100 is not in its simplest form, as both the numerator and denominator are divisible by 20. 40 divided by 20 is equal to two, and 100 divided by 20 is equal to five. This means that the decimal 0.4 and the percentage 40 percent written as a fraction in simplest form is two-fifths or two over five. The correct answer was option (A) 0.4, two-fifths, and 40 percent.

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