NUMBERS - STD 6 mathematics teacher's notes

Question 1: Testing on place values and rounding off

​What is the number 345.8049 rounded off to
the nearest hundredths
A. 345.8          B. 345.80
C. 345.805      D. 345.81 

place values

Solution:

• We will focus our eyes on the most immediate smaller unit than hundredths, and this unit is thousandths.
• We will therefore look at which value represents thousandths, in this case if this value is greater than or equal to 5, then the next value to the left (hundredths) will increase by 1  but in this case, the value of thousandths is 4 which is less than and not equal to 5,
• thus our 0 which represents hundredths could not change. therefore the value 345.8049 when rounded off to the nearest hundredths is 345.80 therefore our answer is B 

QUESTION 2: TESTING ON WRITING words from figures

What is the number 5047532 written in words?
  A.  Five million forty seven hundred five hundred and thirty two
  B.  Five million four hundred and seven thousand and five hundred and thirty-two
  C.  Five million forty seven thousand five hundred and thirty two
  D.  Five hundred and forty seven thousand five hundred and thirty two

Solution:

• The easiest way to pursue this challenge is by separating the number in a group of 3-digits starting from R.H.S [right hand side] thus 5,047,532
• After separating numbers, you will discover that we have made something simpler as shown :
• We will finally compile our answer as: Five million, forty seven thousand, five hundred and thirty two which call [C] as the correct answer

Easy Mathematics- writing numbers in words

Question 3: testing on writing figures from words

Write five million five hundred thousand five hundred and five in symbols?
            A. 5 500 505               B.  5 500 550
            C. 5 005 505             D.  500 505 

Solution:

• The most effective way to solve this challenge is by writing individual numbers by digits then add them together as shown.
• We will now conclude that our answer is 5,500,505 which is [A]

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Easy Mathematics - Writing numbers from figures

Question 4: Testing on total value

 What is the total value of digit 4 in the number 804792?
     A. Forty thousand
     B. Thousands
     C. Four thousand
     D. Ten thousands

Solution:

• One of the easiest way to solve these kind of challenges is by familiarizing yourself with place values. For example: the place value of 4 in question 4 above is thousands. Therefore, we have 4-thousands 
• In total value evaluation we can write as 4000 or four thousand in words. Thus the answer for the question 4 above is [C]

question 5: Testing on Divisibility by 8

 Which of the following numbers is divisible by 8?
           A. 3704        B. 3068
          C. 5018         D. 2124

Solution:

• ​A number passes the test for 8 if the last three digits form a number which is divisible 8
  
• Tip: divide the last three digits by 8, and the number that does not carry a fractional part will be the correct answer.
  
• In this case, our answer could be [a] 3704 because when this number is divided by 8, it returns 463 without the fractional part.

question 6: testing on squares and operations of numbers

 What is the difference in the squares of 25 and 24?
         A. 1                                       B. 2401
        C.49                                      D.1201

Solution:

• Step 1: find the squares of 25 and 24. Thus: 625 and 576
• Step 2: Subtract the square of 24 from the square of 25: thus: 625-576 [the word difference translates to minus]
  • We could therefore boldly say our answer is: 49 which is [C]

question 7: testing on square roots

Work out the square root of 484?
       A. 22                                B. 28
       C. 32                                D. 24

Solution:

1. Step 1: Contemplate the possible value i.e. we know that the square of 20 is 400 and that of 25 is 625, the value 484 therefore is somewhere between 400 and 625. we therefore now know the value can either be 21, 22, 23, or 24.
2. Step 2: Using our number - 484, the right most digit is 4, this means that with the possible values we have [21, 22, 23, or 24], when the right most digit for these values is multiplied by itself, it should provide a 4. example: in case of 21, the right most digit is 1, thus 1 x 1 = 1 this does not give us a 4. we therefore cancel it. Using 23, the number becomes a 9 and 24 brings a 6. This means we remain with one number- 22; is this the number we are looking for?
3. Yes, 22 x 22 = 484. Mission accomplished.

checking for a possible value of a square

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