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FIFTH GRADE / DECIMAL FRACTIONS, PERCENT and RATIO / TEST 1.3

MATHEMATICS IS EASY. PROVIDED THAT ONE WORKS ENOUGH.
ENOUGH IS SKILL DEPENDENT, HAVE TO FIND "ENOUGH" FOR YOUR SIZE.

SOME OF OUR QUESTIONS ARE REALLY HARD, FOR THOSE THAT ARE SKILLED IN MATH.
SKIP THEM IN CASE NOT FOR YOU.

IF YOU DESIRE SO, WE CAN DISCUSS HARD/INTERESTING QUESTIONS IN OUR FORUM.

FRACTION'S UTILITIES

FAST DAS SELBE AUF DEUTSCH
  AS WE HAVE NOTED EARLIER
 ♦ 
MULTIPLICATION IS REPEATED SUMMATION  MODELED COMPACTLY IN TWO DIMENSIONS
 ♦ SO IT IS (PSEUDO) TWO DIMENSIONAL.

THERE ARE TWO GOLDEN RULES:
1. NUMERATORS ARE MULTIPLIED, USED AS THE RESULT'S.
2. DENOMINATORS ARE MULTIPLIED, USED AS THE RESULT'S.
1. Parachutes must slow an object's terminal vertical speed by a minimum 75% in order to be classified as such. The terminal velocity of a skydiver in a face down free-fall position is about 54 m/s . What will be the maximum terminal velocity of a parachute jumper ?

!


a) 13.5 m/s
b) 15.3 m/s
c) 14.7 m/s
d) 17.4 m/s
54 x 1/4 = ?
2. Usain Bolt whose max. speed is 27.79 mph adopted a cheetah whose debated top speed is 75 mph. What is the ratio of Bolt's top speed to cheetah's debated top, considering 2 digits after point ?

!


a) .25
b) .32
c) .45
d) .37
Calculate as .2779 x (4/3) = .0926 x 4 = .0925 x 4 + .0004 , nd drop the last term which is not considered; much easier .
3. The Kangaroo Rat can jump 45 times its own body length. They are longest jumper among all mammals compared to body size. If an adult being 3 inches in body length leaped 8 feet, what is the leap distance to height ratio ?

a) 35
b) 39
c) 32
d) 28
1 foot is 12 inches .
4. It is usually claimed that the best jumper in the world is the Flea. They are longest and highest jumper among animals compared to body size. Fleas can jump 220 times their own body length and 150 times their own body height. If we were to scale up a flea to our size it would be like us jumping nearly 400m in distance and 250m in height. High jump world record is 2.45 m. What is our best performance compared to a scaled flea ?

a) 98 %
b) 9.8 %
c) 0.98 %
d) 0.098 %
2.45/250 = 2.45/2.5 % = 49/50 % = ... .
5. The heaviest land mammal is the African Elephant with a weight around 6500 kg. whereas Bumblebee Bats are the lightest weighing about 2 g. What is the (smaller to bigger) ratio of their weigts?

a) 0.0000003007
b) 0.00000307
c) 0.000000307
d) 0.0000307
2/6 500 000 = ?
y
6. As you see in the previous question our decimal notation is not very convenient to code very small numbers. Which of the followings will be a better alternative to indicate 0.000000307 ?

In case of need for tips get the cursor on "y" or for help click at "ry1/2" .
RY1 RY2



a) 3.07x10-8
b) 3.07x10-7
c) 3.07x10-6
d) 3.07x10-5


Look at ry1 please .
ClickN KIDS Beginning Reading & Spelling Programs Teacher Created Resources ClickN KIDS Beginning Reading & Spelling Programs
7. The Great Pyramid with an height of 147 m. incorporates about 2.3 million stone blocks, weighing an average of 2.5 to 15 tons each. What is the ratio of the number of stones to its height?

!


a) 15646.54
b) 15646.254
c) 15646.2554
d) 15646.25854
2 300 000/147 = ?
8. The base length of the Great Pyramid is calculated as 230.33 meters, according to professor Lehner, and its height once rose to 146.59 meters. What is base length to height ratio ?

a) 1.577
b) 1.71
c) 1.517
d) 1.571
=230.33/146.59 ?
9. If we take half of the smallest top to bottom cross sectional triangle in Great Pyramid we have the measures shown in the figure. What is the hypothenuse to base ratio of this triangle and what is the ratio of this result to Golden ratio ?

!


a) 1.62 and 1.001
b) 1.61 and 1.001
c) 1.62 and 1.0001
d) 1.61 and 1.0001
186.4/115.15 = ? and 1.620/1.618
10. At construction the Great Pyramid was 146 metres tall, but due to erosion its current height is 137 metres. What is in percent height loss ?

a) 6.3
b) 6.1
c) 6.5
d) 7.2
(146-137)/146 = 0.061. Multiply this number by 100.
11. Mesoamerican Pyramids are shorter. The largest pyramid in Mexico is the Great Pyramid of Cholula which is also the largest pyramid by volume in the world. It has a base of 450 by 450 m and a height of 66 m . What is its height to the Great Pyramid of Gizah's height (146 m) ratio ?

!


a) 0.445205479
b) 0.45205479
c) 0.5205479
d) 0.452054
33/73 = ?
y
12. 1.889 = ?

In case of need for tips get the cursor on "y" or for help click at "ry1/2".

RY1 RY2



a) 1.8889
b) 1.9 because it is 17.1/9
c) 1.889 because it is 17.001/9
d) 1.89 because it is 17.01/9
Have please a look at ry1 .
13. Radiocarbon (Carbon-14) dating is a pretty precise method of determining the age of certain archeological artifacts of a biological origin up to about 50,000 years old. The method works because the amount of C-14 decreases to half in about 5730 years, due to radioctive decay .
Let nF/nO denote the ratio of final to original (found in living sample) number of carbon-14 atoms in a fossil. How old should this fossil be if nF/nO = 1/2 ?



a) 3570 years
b) 5370 years
c) 3730 years
d) 5730 years
In 5730 years the number of C-14 atoms drops to half whereas C-12 atoms are all still there, depending of course the amount of the rest . The original ratio is approximately the ratio observed/found in athmosphere.
14. The mammoth tusk in the figure has a nF/nO ratio of 1/128. How old should it be ?

!
a) 40110 years old
b) 45110 years old
c) 30110 years old
d) 35110 years old


In an half-life ratio will be 1/2; in 2 half-lifes it will be 1/2 x 1/2 = 1/4 ... 7 half-lifes should have passed. An half-life is 5730 years ...
15. The female mammoth calf, said to be one of the best-preserved specimens of frozen mammoth ever discovered, is estimated to have been less than one year old before it was preserved in ice about 10,000 years ago. What a nF/nO ratio is to be expected ?

!
a) approximately 1/2
b) approximately 1/4
c) 1/2
d) approximately 1/8
Nearly 2 half-lifes have been over .
16. Atmospheric carbon dioxide (CO2) has a steady-state concentration of about one atom of carbon-14 per every trillion (10-12) atoms of carbon-12. It has been reported that a 22 000 year-old Middle Stone Age camp site with plant food remains from the north-eastern cape has been detected. How many carbon-14 atoms should have a sample having 40 000 trillion C-12 atoms ?



a) approximately 4 000
b) 7000
c) 3500
d) approximately 2 500
About 4 half-times have passed; the C-14 amount decays to 1/16 of the original .
17. Scientist have shown that a Cro-Magnoid individual who lived in Southern Italy 28,000 years ago was a modern European, genetically as well as anatomically. What a nF/nO ratio is to be expected ?

a) 1/64
b) 1/32
c) 1/16
d) 1/128
28 000/5730 = 4.89 which we may taka as 5.
y
18. Not equipped with the mathematical tools we could not calculate the ratios between half-lifes. It will take some time to learn them. We can see though that the fall of C-14 atoms will be along the curve we see in the figure below. What will be the ratio of final number of C-14 atoms to the original ater a time duration of 3/2 half-life has elapsed ?

!
In case of need for tips get the cursor on "y" or for help click at "ry1/2" .
RY1 RY2


a) 375/1000
b) 36/100
c) 4/10
d) 3/10
Please look at ry1 .
19. 0.81 = ?

a) 33/81
b) 27/81
c) 27/33
d) 33/99
81/99 = 27/33 = 9/11
20. 3.933 = ?

a) 3 311/333
b) 5 311/333
c) 3 323/333
d) 5 323/333
Forget about the whole number for a while. 933/999 = 311/333 .
21. 0.4095 = ?

a) 4555/1111
b) 45/1111
c) 455/1111
d) 455/2222
4095/9999 = 1365/3333 = 455/1111 .
y
22. Which choice may be a valid algorithm as we calculate repeating decimals, in case they occur just after the point ?

A:
1- Seperate the repeating-nonrepeating (whole number) parts.
To calculate the repeating part:
2- Count the number of repeating decimals.
3- Write the repeating part as numerator.
4- Write as many 9 as the digits of repeating part.
5- Reduce.
B:
1- Count the number of repeating decimals.
2- Write the repeating part as numerator.
3- Write as many 9 as the digits of repeating part.
4- Reduce.
C:
1- Seperate the repeating-nonrepeating (whole number) parts.
To calculate the repeating part:
2- Count the number of repeating decimals.
3- Write the repeating part as numerator.
4- Write as many 9 as the digits of repeating part.
D:
1- Seperate the repeating-nonrepeating (whole number) parts.
To calculate the repeating part:
2- Count the number of repeating decimals.
3- Write the repeating part as numerator.
4- Reduce.

In case of need for tips get the cursor on "y" or for help click at "ry1/2" .

RY1 RY2



a) A
b) C
c) B
d) D


Have please a look at ry1.
23. 3.08787 = ?

a) 3 8779/9999
b) 3 8779/9999
c) 3 8779/99900
d) 3 8779/99999
This is a really hard question for you. Have a look at ry1 of the previous question, try to imitate and understand. We will revisit the question in 6th grade.
8/100 + 787/99900 is to be calculated . Make use of fractions' utilities in "http://www.test-dr.com/education/5th-Grade-Mathematics/fraction-utilities.html" .
24. Suppose in the previous question "787" reppeats itself billion times and then we have 363. What should we do ?

a) use a computer.
b) treat it like 3.08363
c) treat it like 3.787
d) treat it like 3.08787
No computer can work with this precision. Thank God it is not necessary.
25. 1/100000 x 1/1000000 = ?

a) 1/1000000000
b) 1/10000000000
c) 1/100000000000
d) 1/1000000000000
(54 + 0.07)x(54 + 0.007) = 54x54 + 0.077x54 + 0.07x0.007 = 2916 + 4.158 + 0.00049 = ?
This is the feedback!

THANK YOU FOR YOUR VISIT; HOPE WE COULD BE OF USE.
FOR MUTUAL BENEFIT YOU MAY USE OUR FORUM.
© 2012 , İsmail GERMAN. ALL RIGHTS RESERVED
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