Olympiad Test: Decimals - Class 6 MCQ

Reading the Decimal Number 9.6

• Nine point six: The decimal number 9.6 is read as "nine point six" because the decimal point is pronounced as "point".
• Understanding the Decimal Point: The decimal point separates the whole number from the decimal part. Here, 9 is the whole number and 6 is the decimal part.
• Decimal Places: The number 9.6 has one decimal place. The digit after the decimal represents tenths, so it can also be read as "nine point six tenths."
• Mathematical Representation: Mathematically, 9.6 can be expressed as 9 + 6/10, which equals 9.6.

Decimal form of 4/10:

• Step 1: To convert a fraction to a decimal, divide the numerator by the denominator.
• Step 2: Here, divide 4 by 10.
• Step 3: 4 ÷ 10 = 0.4

Thus, the decimal form of 4/10 is 0.4.

Solution:

• The fraction 3/10 can be expressed as 0.3.
• When we add this to 12, we get:
• 12 + 0.3 = 12.3

Solution:

To convert 46.3 into a fraction, follow these steps:

• Separate the whole number and the decimal: 46.3 is 46 and 0.3.
• Convert the decimal part: 0.3 is the same as 3/10.
• Add the whole number and the fraction: 46 + 3/10.
• To express this as a single fraction, convert 46 into a fraction with a denominator of 10: 46 = 460/10.
• Now combine the fractions: 460/10 + 3/10 = 463/10.

Thus, the fractional form of 46.3 is 463/10.

• Convert fractions to decimals:
  • 8/10 = 0.8
  • 7/1000 = 0.007
• Add the decimals:
  • 0.8 + 0.007 = 0.807
• Conclusion: The sum of 8/10 + 0 + 7/1000 is 0.807.

Solution:

The fraction 4/20 can be simplified to its lowest terms:

• First, divide both the numerator and denominator by their greatest common divisor (GCD), which is 4.
• This gives us: 4 ÷ 4 = 1 and 20 ÷ 4 = 5.
• Thus, 4/20 simplifies to 1/5.

Now, to convert 1/5 into a decimal:

• When you divide 1 by 5, the result is 0.2.

Therefore, the decimal representation of 4/20 is 0.2.

In the number 4.375, the place value of 3 is three-tenths or 0.3.

Here’s how we determine this:

• The digit 3 is located in the tenths place.
• This means its value is calculated as 3 × 1/10 = 0.3.

To determine the decimal fraction represented by the shaded part of the figure:

• Count the total number of sections in the figure.
• Count the number of shaded sections.
• Divide the number of shaded sections by the total number of sections to find the decimal fraction.

In the provided figure:

• Total sections: 10
• Shaded sections: 4

The calculation is as follows:

4 shaded sections ÷ 10 total sections = 0.4

Thus, the decimal fraction represented by the shaded parts is 0.4.

Explanation:

• Given: 7.8 = 7 + 8/?
• To find: The value of ? that makes the equation true.
• Rearranging the equation gives us: 7.8 = 7 + 8/?
• Subtract 7 from both sides: 0.8 = 8/?
• Multiply both sides by ?: 0.8? = 8
• Now, divide both sides by 0.8: ? = 8 / 0.8 = 10
• Thus, the number that should replace the ? is 10.

Answer: B

The correct matching is:

• (i) - [c]
• (ii) - [a]
• (iii) - [d]
• (iv) - [e]
• (v) - [b]

This indicates that:

• Item (i) corresponds to [c]
• Item (ii) corresponds to [a]
• Item (iii) corresponds to [d]
• Item (iv) corresponds to [e]
• Item (v) corresponds to [b]

Thus, the answer is option B.

Explanation:

• Figure A: The shaded part represents 0.3 because there are 3 shaded parts out of a total of 10 parts, which is equivalent to 0.3.
• Figure B: The shaded part represents 0.2 as there are 2 shaded parts out of 10, equating to 0.2.
• Figure C: The shaded part represents 0.4 since there are 4 shaded parts out of 10, which equals 0.4.
• Figure D: The shaded part represents 0.5 because there are 5 shaded parts out of 10, amounting to 0.5.

The equivalent decimal of 0.08 is 0.080.

Solution:

The number 0.7 is greater than 0.08 because:

• 0.7 can be represented as 70/100.
• 0.08 can be represented as 8/100.
• Since 70 is greater than 8, it follows that 0.7 > 0.08.

• Conversion of fraction to decimal: To convert a fraction to a decimal, divide the numerator by the denominator.
• 1/2 = 1 ÷ 2 = 0.5
• Comparison with given options: Compare the decimal value of 1/2 with the options provided.
• Options:
  • A: 0.34
  • B: 0.50
  • C: 0.75
  • D: 3.4
• Correct Answer: Option B: 0.50 is the decimal equivalent of 1/2.

Solution:

To convert Lakshmi's height from centimetres to metres, follow these steps:

• Start with the height in centimetres: 150 cm.
• Use the conversion factor: 1 metre = 100 centimetres.
• Divide the height in centimetres by 100:
• Calculation: 150 cm ÷ 100 = 1.5 m.

Thus, Lakshmi's height is 1.5 metres.

Fractions are represented to the right of the ones place in the place value chart.

• The place value chart extends to accommodate fractions.
• Fractions are positioned after the decimal point.
• This extension allows for the representation of tenths, hundredths, and further decimal places.

In summary, fractions are always found on the right side of the ones place in the place value chart.

The place value of a digit increases by 10 times as it moves from right to left in a place value chart.

This means:

• The first digit is multiplied by 100.
• The next digit is multiplied by 10.
• The following digit is multiplied by 1.
• As you continue to the right, each digit's value is divided by 10.

The decimal point separates the whole number from the fractional part, indicating the transition from ones to tenths.

For example, in the number 243.25:

• 2 is in the hundreds place (2 × 100 = 200).
• 4 is in the tens place (4 × 10 = 40).
• 3 is in the ones place (3 × 1 = 3).
• 2 is in the tenths place (2 × 0.1 = 0.2).
• 5 is in the hundredths place (5 × 0.01 = 0.05).

Thus, the total value is 200 + 40 + 3 + 0.2 + 0.05 = 243.25.

2.078 is the largest decimal among the given numbers. To determine this, we can compare each decimal:

• 0.78
• 1.08
• 2.078
• 0.87
• 0.72

When comparing:

• 2.078 is greater than all the others.
• 1.08 is the next largest.
• 0.87 follows, then 0.78, and finally 0.72.

Thus, the required largest decimal is 2.078.

Expanded form of 78.059:

The expanded form of the number 78.059 can be expressed as:

• 70 (which is 7 multiplied by 10)
• 8 (which is 8 multiplied by 1)
• 0 (which is 0 multiplied by 1/10)
• 5 (which is 5 multiplied by 1/100)
• 9 (which is 9 multiplied by 1/1000)

Thus, the complete expanded form is:

70 + 8 + 0 + 0.05 + 0.009

• Step 1: Add the numbers together:
• 0.3 + 0.03 + 0.003 = 0.333
• Step 2: Thus, the total is 0.333.