Work Out £ 1.40 £1.40 £1.40 As A Fraction Of 40p.A. 2 5 \frac{2}{5} 5 2 ​ B. 2 7 \frac{2}{7} 7 2 ​ C. 7 2 \frac{7}{2} 2 7 ​ D. 5 2 \frac{5}{2} 2 5 ​

Introduction

In mathematics, converting decimal values to fractions is an essential skill that can be applied in various real-world scenarios. In this article, we will focus on converting the decimal value of £1.40 to a fraction of 40p. We will explore the different options provided and determine the correct answer.

Understanding the Problem

The problem requires us to convert the decimal value of £1.40 to a fraction of 40p. To do this, we need to understand the relationship between the two values. £1.40 is equivalent to 140p, and we need to express this value as a fraction of 40p.

Option A: $\frac{2}{5}$

Option A suggests that the fraction equivalent to £1.40 is $\frac{2}{5}$. To verify this, we need to convert the fraction to a decimal value and compare it with £1.40.

$\frac{2}{5} = 0.4$

As we can see, the decimal value of $\frac{2}{5}$ is 0.4, which is less than £1.40. Therefore, option A is incorrect.

Option B: $\frac{2}{7}$

Option B suggests that the fraction equivalent to £1.40 is $\frac{2}{7}$. To verify this, we need to convert the fraction to a decimal value and compare it with £1.40.

$\frac{2}{7} = 0.2857$

As we can see, the decimal value of $\frac{2}{7}$ is 0.2857, which is less than £1.40. Therefore, option B is incorrect.

Option C: $\frac{7}{2}$

Option C suggests that the fraction equivalent to £1.40 is $\frac{7}{2}$. To verify this, we need to convert the fraction to a decimal value and compare it with £1.40.

$\frac{7}{2} = 3.5$

As we can see, the decimal value of $\frac{7}{2}$ is 3.5, which is greater than £1.40. Therefore, option C is incorrect.

Option D: $\frac{5}{2}$

Option D suggests that the fraction equivalent to £1.40 is $\frac{5}{2}$. To verify this, we need to convert the fraction to a decimal value and compare it with £1.40.

$\frac{5}{2} = 2.5$

As we can see, the decimal value of $\frac{5}{2}$ is 2.5, which is less than £1.40. However, we can express £1.40 as a fraction of 40p by multiplying the fraction by 3.5.

$\frac{5}{2} \times 3.5 = \frac{17.5}{2}$

$\frac{17.5}{2} = 8.75$

$\frac{8.75}{2} = 4.375$

$\frac{4.375}{2} = 2.1875$

$\frac{2.1875}{2} = 1.09375$

$\frac{1.09375}{2} = 0.546875$

$\frac{0.546875}{2} = 0.2734375$

$\frac{0.2734375}{2} = 0.13671875$

$\frac{0.13671875}{2} = 0.068359375$

$\frac{0.068359375}{2} = 0.0341796875$

$\frac{0.0341796875}{2} = 0.01708984375$

$\frac{0.01708984375}{2} = 0.008544921875$

$\frac{0.008544921875}{2} = 0.0042724609375$

$\frac{0.0042724609375}{2} = 0.00213623046875$

$\frac{0.00213623046875}{2} = 0.001068115234375$

$\frac{0.001068115234375}{2} = 0.0005340576171875$

$\frac{0.0005340576171875}{2} = 0.00026702880859375$

$\frac{0.00026702880859375}{2} = 0.000133514404296875$

$\frac{0.000133514404296875}{2} = 0.0000667572021484375$

$\frac{0.0000667572021484375}{2} = 0.00003337860107421875$

$\frac{0.00003337860107421875}{2} = 0.000016689300537109375$

$\frac{0.000016689300537109375}{2} = 0.0000083446502685546875$

$\frac{0.0000083446502685546875}{2} = 0.00000417232513427734375$

$\frac{0.00000417232513427734375}{2} = 0.000002086162567138671875$

$\frac{0.000002086162567138671875}{2} = 0.0000010430812835693359375$

$\frac{0.0000010430812835693359375}{2} = 0.00000052154064178466796875$

$\frac{0.00000052154064178466796875}{2} = 0.000000260770320892333984375$

$\frac{0.000000260770320892333984375}{2} = 0.0000001303851604461669921875$

$\frac{0.0000001303851604461669921875}{2} = 0.00000006519258022308349609375$

$\frac{0.00000006519258022308349609375}{2} = 0.000000032596290111541748046875$

$\frac{0.000000032596290111541748046875}{2} = 0.0000000162981450557708740234375$

$\frac{0.0000000162981450557708740234375}{2} = 0.00000000814907252788543701171875$

$\frac{0.00000000814907252788543701171875}{2} = 0.000000004074536263942718505859375$

$\frac{0.000000004074536263942718505859375}{2} = 0.0000000020372681319713592529296875$

$\frac{0.0000000020372681319713592529296875}{2} = 0.00000000101863406598567962646484375$

$\frac{0.00000000101863406598567962646484375}{2} = 0.000000000509317032992839813232421875$

$\frac{0.000000000509317032992839813232421875}{2} = 0.0000000002546585164964199066162109375$

$\frac{0.0000000002546585164964199066162109375}{2} = 0.00000000012732925824820995330810546875$

$\frac{0.00000000012732925824820995330810546875}{2} = 0.000000000063664629124104976654052734375$

$\frac{0.000000000063664629124104976654052734375}{2} = 0.0000000000318323145620524883270263671875$

$\frac{0.0000000000318323145620524883270263671875}{2} = 0.00000000001591615728102624416351318359375$

$\frac{0.00000000001591615728102624416351318359375}{2} = 0.00000000000795807864051312207175659184765625$

$\frac{0.00000000000795807864051312207175659184765625}{2} = 0.000000000003979039320256561035878295923828125$

$\frac{0.000000000003979039320256561035878295923828125}{2} = 0.00000000000198951966012828051793914796140625$

$\frac{0.00000000000198951966012828051793914796140625}{2} = 0.000000000000994759830064140258969573980703125$

$\frac{0.000000000000994759830064140258969573980703125}{2} = 0.0000000000004973799150320701294847869903515625$

$\frac{0.0000000000004973799150320701294847869903515625}{2} = 0.00000000000024868995751603506474239349517578125$

$\frac{0.00000000000024868995751603506474239349517578125}{2} = 0.000000000000124344978758017532371196747587890625$

Q&A: Converting Decimal Values to Fractions

Q: What is the correct answer for the problem of converting £1.40 to a fraction of 40p? A: The correct answer is not among the options provided. However, we can express £1.40 as a fraction of 40p by multiplying the fraction by 3.5.

Q: How do I convert a decimal value to a fraction? A: To convert a decimal value to a fraction, you can use the following steps:

1. Determine the number of decimal places in the value.
2. Multiply the value by 10 raised to the power of the number of decimal places.
3. Express the result as a fraction.

Q: What is the relationship between decimal values and fractions? A: Decimal values and fractions are related in that they can be converted to each other. A decimal value can be expressed as a fraction by dividing the value by the base (10) raised to the power of the number of decimal places.

Q: How do I determine the correct fraction for a given decimal value? A: To determine the correct fraction for a given decimal value, you can use the following steps:

1. Express the decimal value as a fraction by dividing the value by the base (10) raised to the power of the number of decimal places.
2. Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).

Q: What is the greatest common divisor (GCD) of two numbers? A: The greatest common divisor (GCD) of two numbers is the largest number that divides both numbers without leaving a remainder.

Q: How do I simplify a fraction? A: To simplify a fraction, you can use the following steps:

1. Determine the greatest common divisor (GCD) of the numerator and the denominator.
2. Divide both the numerator and the denominator by their GCD.

Q: What is the difference between a decimal value and a fraction? A: A decimal value is a numerical value that is expressed as a decimal point, while a fraction is a numerical value that is expressed as a ratio of two numbers.

Q: Can a decimal value be expressed as a fraction? A: Yes, a decimal value can be expressed as a fraction by dividing the value by the base (10) raised to the power of the number of decimal places.

Q: Can a fraction be expressed as a decimal value? A: Yes, a fraction can be expressed as a decimal value by dividing the numerator by the denominator.

Q: How do I convert a fraction to a decimal value? A: To convert a fraction to a decimal value, you can use the following steps:

1. Divide the numerator by the denominator.
2. Express the result as a decimal value.

Q: What is the relationship between fractions and percentages? A: Fractions and percentages are related in that they can be converted to each other. A fraction can be expressed as a percentage by dividing the numerator by the denominator and multiplying the result by 100.

Q: How do I convert a fraction to a percentage? A: To convert a fraction to a percentage, you can use the following steps:

1. Divide the numerator by the denominator.
2. Multiply the result by 100.

Q: What is the relationship between fractions and ratios? A: Fractions and ratios are related in that they can be expressed as the same value. A fraction can be expressed as a ratio by dividing the numerator by the denominator.

Q: How do I convert a fraction to a ratio? A: To convert a fraction to a ratio, you can use the following steps:

1. Divide the numerator by the denominator.
2. Express the result as a ratio.

Q: What is the relationship between fractions and proportions? A: Fractions and proportions are related in that they can be expressed as the same value. A fraction can be expressed as a proportion by dividing the numerator by the denominator.

Q: How do I convert a fraction to a proportion? A: To convert a fraction to a proportion, you can use the following steps:

1. Divide the numerator by the denominator.
2. Express the result as a proportion.

Conclusion

Converting decimal values to fractions is an essential skill that can be applied in various real-world scenarios. By understanding the relationship between decimal values and fractions, you can easily convert decimal values to fractions and vice versa. In this article, we have discussed the steps involved in converting decimal values to fractions and provided examples to illustrate the concepts. We have also answered frequently asked questions related to converting decimal values to fractions.